Multiobjective Tuning and Performance Assessment of PID Using Teaching–Learning-Based Optimization

There have been many studies on the optimal tuning and control performance assessment (CPA) of the PID controller. In the optimal tuning, the trade-off between the setpoint tracking and the disturbance rejection performance is a challenge. Minimum output variance (MOV) is very widely used as a benchmark for CPA of PID, but it is difficult to be observed due to the non-convex optimization problem. In this paper, a new multiobjective function, considering both the OV in the CPA problem and integral of absolute error, is proposed to tune PID for this trade-off. The CPA-related non-convex problem and tuning-related multiobjective problem are solved by teaching–learning-based optimization, which guarantees a tighter lower bound for MOV due to the excellent capability of local optima avoidance and has higher computational efficiency due to the low complexity. The numerical examples of CPA problems show that the algorithm can generate better MOV than existing methods with less calculation time. The relationship between the weight of the multiobjective function and the performance, including setpoint tracking, stochastic and step disturbance rejection, is revealed by simulation results of the tuning method applied to two temperature control systems. The proper adjustment of the weight with a multistage strategy can achieve the trade-off to obtain excellent setpoint tracking performance in the initial stage and satisfying disturbance rejection performance in the steady stage.